Details

sample419.0ms

Algorithm

intervals

Results

101.0ms	46×	body	640	valid
85.0ms	70×	body	1280	valid
51.0ms	254×	body	80	valid
14.0ms	22×	body	320	valid
3.0ms	8×	body	160	valid
2.0ms	1×	body	2560	valid

simplify3.4s

Counts

1 → 1

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	19	784
1	35	654
2	62	654
3	95	654
4	210	654
5	823	654
done	5000	654

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y.re (log (hypot x.re x.im)))
1.4b	(* (atan2 x.im x.re) y.re)
1.4b	(* (atan2 x.im x.re) y.im)
32.4b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
10×	`add-cbrt-cube` `associate-r` `add-exp-log`
9×	`associate-l`
6×	`log-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sin-sum` `log-pow` `fma-udef`

Counts

4 → 77

Calls

4 calls:

13.0ms	(* y.re (log (hypot x.re x.im)))
10.0ms	(* (atan2 x.im x.re) y.re)
10.0ms	(* (atan2 x.im x.re) y.im)
7.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(* y.re (log (hypot x.re x.im)))
38.0ms	(* (atan2 x.im x.re) y.re)
33.0ms	(* (atan2 x.im x.re) y.im)
308.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.7s

Counts

89 → 89

Iterations

Useful iterations: 3 (920.0ms)

Iter	Nodes	Cost
0	138	25555
1	270	25013
2	639	24891
3	1889	24546
done	5003	24546

prune834.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.8b

localize90.0ms

Local error

Found 4 expressions with local error:

4.7b	(cbrt (atan2 x.im x.re))
4.7b	(cbrt (atan2 x.im x.re))
4.7b	(cbrt (atan2 x.im x.re))
32.4b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`sin-sum` `fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
1.0ms	(cbrt (atan2 x.im x.re))
2.0ms	(cbrt (atan2 x.im x.re))
4.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series448.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(cbrt (atan2 x.im x.re))
68.0ms	(cbrt (atan2 x.im x.re))
78.0ms	(cbrt (atan2 x.im x.re))
228.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify3.5s

Counts

61 → 61

Iterations

Useful iterations: 3 (103.0ms)

Iter	Nodes	Cost
0	57	22262
1	91	20817
2	148	20700
3	256	20155
4	619	20155
5	1784	20155
done	5000	20155

prune643.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.8b

localize133.0ms

Local error

Found 4 expressions with local error:

4.7b	(cbrt (atan2 x.im x.re))
4.7b	(cbrt (atan2 x.im x.re))
4.7b	(cbrt (atan2 x.im x.re))
32.4b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`sin-sum` `fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
1.0ms	(cbrt (atan2 x.im x.re))
1.0ms	(cbrt (atan2 x.im x.re))
3.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(cbrt (atan2 x.im x.re))
69.0ms	(cbrt (atan2 x.im x.re))
79.0ms	(cbrt (atan2 x.im x.re))
261.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify3.2s

Counts

61 → 61

Iterations

Useful iterations: 3 (124.0ms)

Iter	Nodes	Cost
0	57	22262
1	91	20817
2	148	20700
3	256	20155
4	619	20155
5	1784	20155
done	5000	20155

prune644.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.8b

localize119.0ms

Local error

Found 4 expressions with local error:

7.2b	(cbrt (* (atan2 x.im x.re) y.re))
7.2b	(cbrt (* (atan2 x.im x.re) y.re))
7.2b	(cbrt (* (atan2 x.im x.re) y.re))
32.7b	(sin (fma (log (hypot x.re x.im)) y.im (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
1×	`sin-sum` `fma-udef`

Counts

4 → 43

Calls

4 calls:

5.0ms	(cbrt (* (atan2 x.im x.re) y.re))
5.0ms	(cbrt (* (atan2 x.im x.re) y.re))
5.0ms	(cbrt (* (atan2 x.im x.re) y.re))
4.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))

series510.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(cbrt (* (atan2 x.im x.re) y.re))
89.0ms	(cbrt (* (atan2 x.im x.re) y.re))
75.0ms	(cbrt (* (atan2 x.im x.re) y.re))
251.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))

simplify4.6s

Counts

55 → 55

Iterations

Useful iterations: 6 (3.2s)

Iter	Nodes	Cost
0	71	22960
1	119	22931
2	194	22811
3	373	20506
4	796	19960
5	1868	18967
6	4951	18850
done	5000	18850

prune528.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.8b

regimes485.0ms

Accuracy

0% (0.3b remaining)

Error of 3.9b against oracle of 3.5b and baseline of 3.9b

bsearch0.0ms

simplify12.0ms

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	21	974
1	28	974
done	28	974

end0.0ms

sample8.7s

Algorithm

intervals

Results

3.1s	7928×	body	80	valid
2.9s	2187×	body	1280	valid
1.5s	1402×	body	640	valid
367.0ms	569×	body	320	valid
95.0ms	40×	body	2560	valid
95.0ms	263×	body	160	valid